So in other words you are going on a different sort of tantrum!
One more in line with say, a mother not wanting her son's lead part in the school play to have any of it's spot light shared.
It's admirable in a way but all together somewhat petty imho. If this was just a matter of assuming poor quality in the film that would be one thing but this comes off to me as something else. If Sherlock and Batman had a cross over I can see similar such fanboy concerns being raised.
Who cares about what causes the(much appreciated) buzz, it's the film you should be concerned with. This same thing happens every time a new popular villain is announced for a role(see venom/joker/doc ock/Bane/catwomen). It's a combination of the newer element garnering the attention.
Problem?
Ignoring that lex is an enemy to both in the material(much like joker was an enemy to both dent and batman). Joker was an enemy to everyone in that film(even his own men) but there was one key point that made him batman's arch enemy. Joker never shut up about batman and his particular rhetoric against him. He messed with everyone(dent in the hospital) but it was batman on his mind. Now granted, joker is sort of a singular focused obsessive individual in that way, but I'm pretty sure when lex starts his diatribe about the alien a similar effect will be achieved.
Also, all the film has to do begin with Luthor's motivations squarely aimed at the Man of Steel alien.
30 years of movies(and tv shows) where our culture has been conditioned to understand that Lex is superman's arch enemy over and over and you worry that now that bat's is in the picture there will be a failure to communicate? Meh, if anything it will be a welcomed changed imo. I love when Bruce puts his attention on Lex(the real bruce not that nolan creature).
You really think that

There is a lot of sensationalism in that comparison. Just seems like a bad and overblown example.
-Xmen 3 was a spit in the face to the character in every way(including killing him off in the first 3 mins). Will Superman might be killed off in the first 3 minutes in an adaptation of one of his most famous and specific arcs? Also Cyclops was replaced as the leader to the xmen...
-Xmen 2 Cyclops was taken out a quarter into the film...
-Xmen 1...meh not bad. Had his girl flirted with, I like that idea tbh.
That's what your comparison evokes, I think it's a bit much.
Point being I just think if you honestly have that fear than you should rest easy. Ignoring all other things, Cyclops didn't have his name in the title. Moreover, the producers weren't calling cyclops the "king daddy of superheroes" or "the pillar/totem/top of the pyramid of the universe"
Relax
I thought Frank was writing batman stories though?
What's wrong with how Timm does it?
Pretty sure if they look at the recent dcu comics, they will be fine.
Speak for yourself.
You clearly are a particular kind of fan.
Here's the thing, let's just say you are right in your many theories above and batman get's the better of superman and lex isn't portrayed as superman sworn enemy and some or even lots of focus is "taken away from superman".
To then imply that the ONLY people that are likely to get something from this film are Batman fans? I'm pretty sure even the pa kent fans....even the hulk fans will get something out of this.
This leads me to my analogy of the stage play mom and her child in the lead. It's evocative of a sort of entitlement. It would be one thing to question if the superman character will get appropriate story focus for development, but that's not what I'm reading in your posts(sorry if I'm mistaken).
This is one step removed from the popular mentality during DC/Marvel crossovers
I suppose this acceptable, superman fans have been trough a lot